Beck was awarded the Fulkerson Prize in 1985 for a paper titled "Roth's estimate of the discrepancy of integer sequences is nearly sharp",[3] which introduced the notion of discrepancy on hypergraphs and established an upper bound on the discrepancy of the family of arithmetic progressions contained in {1,2,...,n}, matching the classical lower bound up to a polylogarithmic factor. Jiří Matoušek and Joel Spencer later succeeded in getting rid of this factor, showing that the bound was really sharp.